Estimating the Effective Reproduction Number of COVID-19 by Country
Louis Rossouw
2021-05-14 10:00:03 GMT
1 Introduction
This paper contains estimates for the effective reproduction number \(R_{t,m}\) over time \(t\) in various countries \(m\) of the world. This is done using the methodology as described in [1]. These have been implemented in R using EpiEstim package [2] which is what is used here. The methodology and assumptions are described in more detail here.
This paper and it’s results should be updated roughly daily and is available online.
As this paper is updated over time this section will summarise significant changes. The code producing this paper is tracked using Git. The Git commit hash for this project at the time of generating this paper was d3bde1ab07427bfb27f06581746d9b4e3ade6bd0.
2 Data
Data are downloaded from [3]. Minor formatting is applied to get the data ready for further processing.
3 Basic Exploration
Below cumulative case count is plotted on a log scale by continent.
Cumulative Reported Cases by Continent
Below a 7-day moving average of daily case count is plotted on a log scale by continent.
Daily Reported Cases by Continent (7-day moving average)
Below cumulative deaths by country is plotted on a log scale:
Cumulative Reported Deaths by Continent
Below a 7-day moving average of daily deaths by country is plotted on a log scale:
Daily Deaths by Continent (7-day moving average)
4 Method & Assumptions
The methodology is described in detail here.
Countries with populations of less than 500 000 are excluded.
5 Results
5.1 World-wide
| Estimated Type | Daily Count (Last Week) | Week Ending | R - Lower CI | R - Mean | R - Uppper CI |
|---|---|---|---|---|---|
| cases | 729,345.6 | 2021-05-13 | 0.9 | 0.9 | 0.9 |
| deaths | 12,610.4 | 2021-05-13 | 1.0 | 1.0 | 1.0 |
5.2 Current reproduction number estimates by country
Below current (last weekly) \(R_{t,m}\) estimates are plotted on a world map.
5.2.0.1 Cases
5.2.1 Deaths
5.3 Top 10 countries
Below we show various extremes of \(R_{t,m}\) where counts (deaths or cases) exceed 10 per day in the last week.
5.3.1 Lowest \(R_{t,m}\) based on deaths
| Country | Estimated Type | Daily Count (Last Week) | Week Ending | R - Lower CI | R - Mean | R - Uppper CI |
|---|---|---|---|---|---|---|
| North Macedonia | deaths | 18.0 | 2021-05-13 | 0.6 | 0.7 | 0.8 |
| Moldova | deaths | 11.9 | 2021-05-13 | 0.6 | 0.7 | 0.9 |
| Bangladesh | deaths | 40.0 | 2021-05-13 | 0.7 | 0.7 | 0.8 |
| Serbia | deaths | 16.0 | 2021-05-13 | 0.6 | 0.8 | 0.9 |
| Bosnia and Herzegovina | deaths | 28.0 | 2021-05-13 | 0.7 | 0.8 | 0.9 |
| Belgium | deaths | 28.7 | 2021-05-13 | 0.7 | 0.8 | 0.9 |
| Austria | deaths | 15.9 | 2021-05-13 | 0.6 | 0.8 | 0.9 |
| Hungary | deaths | 96.1 | 2021-05-13 | 0.7 | 0.8 | 0.9 |
| Palestine | deaths | 10.7 | 2021-05-13 | 0.6 | 0.8 | 1.0 |
| Greece | deaths | 59.9 | 2021-05-13 | 0.7 | 0.8 | 0.9 |
5.3.2 Lowest \(R_{t,m}\) based on cases
| Country | Estimated Type | Daily Count (Last Week) | Week Ending | R - Lower CI | R - Mean | R - Uppper CI |
|---|---|---|---|---|---|---|
| Somalia | cases | 16.9 | 2021-05-13 | 0.2 | 0.3 | 0.3 |
| Kosovo | cases | 89.9 | 2021-05-13 | 0.3 | 0.3 | 0.4 |
| Djibouti | cases | 11.7 | 2021-05-13 | 0.3 | 0.4 | 0.5 |
| Botswana | cases | 89.1 | 2021-05-13 | 0.4 | 0.4 | 0.5 |
| Oman | cases | 481.3 | 2021-05-13 | 0.6 | 0.6 | 0.6 |
| Yemen | cases | 11.6 | 2021-05-13 | 0.5 | 0.6 | 0.7 |
| Mali | cases | 17.1 | 2021-05-13 | 0.5 | 0.6 | 0.7 |
| Israel | cases | 33.0 | 2021-05-13 | 0.5 | 0.6 | 0.7 |
| Turkey | cases | 15,144.9 | 2021-05-13 | 0.6 | 0.6 | 0.7 |
| Palestine | cases | 411.9 | 2021-05-13 | 0.6 | 0.6 | 0.7 |
5.3.3 Highest \(R_{t,m}\) based on deaths
| Country | Estimated Type | Daily Count (Last Week) | Week Ending | R - Lower CI | R - Mean | R - Uppper CI |
|---|---|---|---|---|---|---|
| Sudan | deaths | 11.6 | 2021-05-13 | 1.5 | 2.6 | 4.6 |
| Nepal | deaths | 133.9 | 2021-05-13 | 2.0 | 2.5 | 3.0 |
| Sri Lanka | deaths | 21.0 | 2021-05-13 | 1.3 | 1.5 | 1.8 |
| Japan | deaths | 97.6 | 2021-05-13 | 1.2 | 1.4 | 1.5 |
| Malaysia | deaths | 25.4 | 2021-05-13 | 1.1 | 1.3 | 1.5 |
| Costa Rica | deaths | 24.7 | 2021-05-13 | 1.1 | 1.3 | 1.5 |
| South Africa | deaths | 56.0 | 2021-05-13 | 1.1 | 1.2 | 1.4 |
| Thailand | deaths | 26.0 | 2021-05-13 | 1.0 | 1.2 | 1.4 |
| Honduras | deaths | 50.1 | 2021-05-13 | 1.1 | 1.2 | 1.4 |
| Georgia | deaths | 21.7 | 2021-05-13 | 1.0 | 1.1 | 1.3 |
5.3.4 Highest \(R_{t,m}\) based on cases
| Country | Estimated Type | Daily Count (Last Week) | Week Ending | R - Lower CI | R - Mean | R - Uppper CI |
|---|---|---|---|---|---|---|
| Papua New Guinea | cases | 230.3 | 2021-05-13 | 1.9 | 2.6 | 3.0 |
| Oceania | cases | 246.1 | 2021-05-13 | 1.8 | 2.3 | 2.6 |
| Vietnam | cases | 92.9 | 2021-05-13 | 1.6 | 2.0 | 2.5 |
| Benin | cases | 15.9 | 2021-05-13 | 1.4 | 1.8 | 2.2 |
| Maldives | cases | 1,134.3 | 2021-05-13 | 1.5 | 1.7 | 1.8 |
| Taiwan | cases | 11.9 | 2021-05-13 | 1.3 | 1.7 | 2.1 |
| Gabon | cases | 76.1 | 2021-05-13 | 1.2 | 1.4 | 1.6 |
| Dominican Republic | cases | 733.6 | 2021-05-13 | 1.3 | 1.4 | 1.5 |
| Timor | cases | 144.1 | 2021-05-13 | 1.2 | 1.3 | 1.4 |
| South Africa | cases | 2,126.0 | 2021-05-13 | 1.3 | 1.3 | 1.4 |
5.4 Risk Quadrants
The plots below show weekly cases (or deaths) on the X-axis and the reproduction number on the Y-axis. By dividing this into 4 quadrants we can identify countries with high cases and high reproduction numbers, or high cases and low reproduction numbers etc.
Values where the reproduction number exceeds 3 are plotted at 3.
5.4.1 Cases
Risk Quadrants - Cases
5.4.2 Deaths
Risk Quadrants - Deaths
5.5 Country Plots by Continent
Below we plot results for each country/province in a list. Values larger than 3 are plotted at 3.
5.5.1 Africa
5.5.1.1 Algeria
5.5.1.2 Angola
5.5.1.3 Benin
5.5.1.4 Botswana
5.5.1.5 Burkina Faso
5.5.1.6 Burundi
5.5.1.7 Cameroon
5.5.1.8 Cape Verde
5.5.1.9 Central African Republic
5.5.1.10 Chad
5.5.1.11 Comoros
5.5.1.12 Congo
5.5.1.13 Cote d’Ivoire
5.5.1.14 Democratic Republic of Congo
5.5.1.15 Djibouti
5.5.1.16 Egypt
5.5.1.17 Equatorial Guinea
5.5.1.18 Eritrea
5.5.1.19 Eswatini
5.5.1.20 Ethiopia
5.5.1.21 Gabon
5.5.1.22 Gambia
5.5.1.23 Ghana
5.5.1.24 Guinea
5.5.1.25 Guinea-Bissau
5.5.1.26 Kenya
5.5.1.27 Lesotho
5.5.1.28 Liberia
5.5.1.29 Libya
5.5.1.30 Madagascar
5.5.1.31 Malawi
5.5.1.32 Mali
5.5.1.33 Mauritania
5.5.1.34 Mauritius
5.5.1.35 Morocco
5.5.1.36 Mozambique
5.5.1.37 Namibia
5.5.1.38 Niger
5.5.1.39 Nigeria
5.5.1.40 Rwanda
5.5.1.41 Senegal
5.5.1.42 Sierra Leone
5.5.1.43 Somalia
5.5.1.44 South Africa
5.5.1.45 South Sudan
5.5.1.46 Sudan
5.5.1.47 Togo
5.5.1.48 Tunisia
5.5.1.49 Uganda
5.5.1.50 Zambia
5.5.1.51 Zimbabwe
5.5.2 Asia
5.5.2.1 Afghanistan
5.5.2.2 Armenia
5.5.2.3 Azerbaijan
5.5.2.4 Bahrain
5.5.2.5 Bangladesh
5.5.2.6 Bhutan
5.5.2.7 Cambodia
5.5.2.8 China
5.5.2.9 Georgia
5.5.2.10 India
5.5.2.11 Indonesia
5.5.2.12 Iran
5.5.2.13 Iraq
5.5.2.14 Israel
5.5.2.15 Japan
5.5.2.16 Jordan
5.5.2.17 Kazakhstan
5.5.2.18 Kuwait
5.5.2.19 Kyrgyzstan
5.5.2.20 Laos
5.5.2.21 Lebanon
5.5.2.22 Malaysia
5.5.2.23 Maldives
5.5.2.24 Mongolia
5.5.2.25 Myanmar
5.5.2.26 Nepal
5.5.2.27 Oman
5.5.2.28 Pakistan
5.5.2.29 Palestine
5.5.2.30 Philippines
5.5.2.31 Qatar
5.5.2.32 Saudi Arabia
5.5.2.33 Singapore
5.5.2.34 South Korea
5.5.2.35 Sri Lanka
5.5.2.36 Syria
5.5.2.37 Taiwan
5.5.2.38 Thailand
5.5.2.39 Timor
5.5.2.40 Turkey
5.5.2.41 United Arab Emirates
5.5.2.42 Uzbekistan
5.5.2.43 Vietnam
5.5.2.44 Yemen
5.5.3 Europe
5.5.3.1 Albania
5.5.3.2 Austria
5.5.3.3 Belarus
5.5.3.4 Belgium
5.5.3.5 Bosnia and Herzegovina
5.5.3.6 Bulgaria
5.5.3.7 Croatia
5.5.3.8 Cyprus
5.5.3.9 Czechia
5.5.3.10 Denmark
5.5.3.11 Estonia
5.5.3.12 Finland
5.5.3.13 France
5.5.3.14 Germany
5.5.3.15 Greece
5.5.3.16 Hungary
5.5.3.17 Ireland
5.5.3.18 Italy
5.5.3.19 Kosovo
5.5.3.20 Latvia
5.5.3.21 Lithuania
5.5.3.22 Luxembourg
5.5.3.23 Moldova
5.5.3.24 Montenegro
5.5.3.25 Netherlands
5.5.3.26 North Macedonia
5.5.3.27 Norway
5.5.3.28 Poland
5.5.3.29 Portugal
5.5.3.30 Romania
5.5.3.31 Russia
5.5.3.32 Serbia
5.5.3.33 Slovakia
5.5.3.34 Slovenia
5.5.3.35 Spain
5.5.3.36 Sweden
5.5.3.37 Switzerland
5.5.3.38 Ukraine
5.5.3.39 United Kingdom
5.5.4 North America
5.5.4.1 Canada
5.5.4.2 Costa Rica
5.5.4.3 Cuba
5.5.4.4 Dominican Republic
5.5.4.5 El Salvador
5.5.4.6 Guatemala
5.5.4.7 Haiti
5.5.4.8 Honduras
5.5.4.9 Jamaica
5.5.4.10 Mexico
5.5.4.11 Nicaragua
5.5.4.12 Panama
5.5.4.13 Trinidad and Tobago
5.5.4.14 United States
5.5.5 Oceania
5.5.5.1 Australia
5.5.5.2 New Zealand
5.5.5.3 Papua New Guinea
5.5.6 South America
5.5.6.1 Argentina
5.5.6.2 Bolivia
5.5.6.3 Brazil
5.5.6.4 Chile
5.5.6.5 Colombia
5.5.6.6 Ecuador
5.5.6.7 Guyana
5.5.6.8 Paraguay
5.5.6.9 Peru
5.5.6.10 Suriname
5.5.6.11 Uruguay
5.5.6.12 Venezuela
5.6 Detailed Output
Detailed output for all countries are saved to a comma-separated value file. The file can be found here.
6 Discussion
Limitation of this method to estimate \(R_{t,m}\) are noted in [1]
- It’s sensitive to changes in transmissibility, changes in contact patterns, depletion of the susceptible population and control measures.
- It relies on an assumed generation interval assumptions.
- The size of the time window can affect the volatility of results.
- Results are time lagged with regards to true infection, more so in the case of the use of deaths.
- It’s sensitive to changes in case (or death) detection.
- The generation interval may change over time.
Further to the above the estimates are made under assumption that the cases and deaths are reported consistently over time. For cases this means that testing needs to be at similar levels and reported with similar lag. Should these change rapidly over an interval of a few weeks the above estimates of the effective reproduction numbers would be biased. For example a rapid expansion of testing over the last 3 weeks would results in overestimating recent effective reproduction numbers. Similarly any changes in reporting (over time and underreporting) of deaths would also bias estimates of the reproduction number estimated using deaths.
Estimates for the reproduction number are plotted in time period in which the relevant measure is recorded. Though in reality the infections giving rise to those estimates would have occurred roughly between a week to 4 weeks earlier depending on whether it was cases or deaths. These figures have not been shifted back.
Despite these limitation we believe the ease of calculation of this method and the ability to use multiple sources makes it useful as a monitoring tool.